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Applying the Poincar\u00e9\u2013Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.<\/jats:p>","DOI":"10.1142\/s0218127414400112","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T08:35:53Z","timestamp":1409301353000},"page":"1440011","source":"Crossref","is-referenced-by-count":6,"title":["Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type"],"prefix":"10.1142","volume":"24","author":[{"given":"Amadeu","family":"Delshams","sequence":"first","affiliation":[{"name":"Dep. de Matem\u00e0tica Aplicada I, Universitat Polit\u00e8cnica de Catalunya, Av. 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